Pythagorean Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c². Rearrange the formula to solve for the missing side.

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. It is the opposite operation of squaring a number.

Front

Do the lengths 15, 12, and 9 form a right triangle?

Back

Yes, because 15² = 12² + 9² (225 = 144 + 81).

Front

What is the formula to calculate the area of a right triangle?

Back

Area = (1/2) * base * height.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 : √3 : 2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

If one side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.